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Title: Airfoil design via optimal control theory
Authors: Yiu, KFC
Mak, KL
Teo, KL
Keywords: Airfoil design
Optimal control
Finite elements
Full potential equation
Issue Date: 2005
Publisher: American Institute of Mathematical Sciences
Source: Journal of industrial and management optimization, 2005, v. 1, no. 1, p. 133-148 How to cite?
Journal: Journal of industrial and management optimization 
Abstract: In airfoil design, one problem of great interest is to find the target airfoil profile to achieve a given target velocity distribution. It can be formulated as an optimal control problem, with the control being the airfoil profile and the governing equation being the full potential equation in the transonic regime. To discretize the problem, one approach is to employ the finite element method. In the discretized space, a direct relationship between the objective function and the unknown profile co-ordinates can be defined via the finite element basis functions. Moreover, it is advantageous to derive the gradient in the discretized space rather than the continuous space to avoid contamination by discretization errors. In this paper, this approach is studied. In particular, a new formulation is proposed. A novel decomposition of the discrete space for the potential function, the gradient is derived and an efficient algorithm using the quasi-Newton method is described. In generating and adjusting the mesh during iterations, the elliptic mesh generation technique is used.
ISSN: 1547-5816
EISSN: 1553-166X
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